Impact of Network Topology Knowledge on Fairness: A Geometric Approach

In this paper, we examine how the precision of network topology knowledge impacts the achievable degree of max-min fairness. We focus on time-division multiple access (TDMA) networks, and employ a model based on physical-layer events that sufficiently describes the topology effects with respect to TDMA. Using Jain's fairness index, our key contribution is a characterization of the fairness loss resulting from allocation of resources (in our case time-divisions) based on imprecise knowledge of topology. We find loss is more pronounced when a single link has low signal-to-noise ratio (SNR); i.e. links which have poor throughput also make the allocation more unfair. Conversely, our analysis suggests that if the relative error in estimating link qualities is identical for all links in the network, no one link dominates the fairness loss.